Simulation optimization method for running speed curve of maglev train based on virtual speed limit

Abstract

The application provides a virtual speed limit based maglev train operation speed curve simulation optimization method, proposes a time-space domain hybrid adaptive discretization method, can dynamically switch time domain and space domain calculation modes according to train speed, guarantees time resolution in the low speed section, keeps space resolution in the high speed section, fundamentally eliminates the speed dependent error caused by the single domain method, and realizes the consistency of numerical accuracy in the whole speed domain. In addition, the application introduces virtual speed limit as the core decision variable, converts the complex high-dimensional continuous control problem into a structured discrete input sequence problem, realizes the indirect control of the traction, cruise, coasting and braking process by adjusting the virtual speed limit distribution, and significantly reduces the optimization dimension. With the virtual speed limit block division mechanism and the embedded constraint processing strategy, the method can automatically generate a physically feasible optimal speed curve under the conditions of double speed protection, safe braking distance and passenger comfort and the like.

Description

Technical Field

[0001] This invention relates to the field of maglev train zone control system technology, and in particular to a simulation optimization method for maglev train operating speed curve based on virtual speed limit. Background Technology

[0002] With the acceleration of global urbanization and the increasing demand for efficient and environmentally friendly transportation, maglev trains, as an advanced rail transit technology, are gradually becoming an important part of the transportation systems of major cities and regions due to their significant advantages such as low noise, high speed, small turning radius, strong climbing ability, and low maintenance costs. Compared with traditional wheel-rail trains, maglev trains achieve levitation and guidance through electromagnetic force, reducing direct contact with the track, thereby significantly reducing friction loss and improving operating efficiency and passenger comfort.

[0003] In the operation and management of maglev systems, optimizing the train speed curve is one of the key aspects of improving the overall system performance. The speed curve directly affects not only the train's operational safety, operating time, and energy consumption, but also passenger comfort. By optimizing the speed curve, the energy consumption of the traction power supply system can be significantly reduced while meeting operating time and safety requirements, thereby improving the economy and sustainability of the maglev system.

[0004] However, optimizing the speed curve of maglev trains faces numerous challenges. First, during maglev train operation, there is a strong coupling relationship between electrical and motion variables. The traction power supply system needs to dynamically adjust the amplitude, phase, and frequency of current and voltage according to the real-time operating status of the train to meet the power requirements of different operating stages. Second, maglev systems typically employ a multi-segment power supply mode, with different sections potentially using single-end or double-end power supply methods, further increasing the system's complexity. Furthermore, multiple constraints must be considered during train operation, including maximum speed limits, dual-speed protection (such as emergency braking and safe coasting under power loss), and passenger comfort (such as acceleration impact rate limits). These factors collectively determine the complexity and difficulty of speed curve optimization.

[0005] Against the backdrop of global advocacy for energy conservation, emission reduction, and sustainable development, improving the energy efficiency of maglev transportation systems has become a common goal in the industry. How to design the optimal speed curve within a limited operating time through precise modeling and comprehensive scheduling of traction and levitation energy consumption, thereby reducing the output energy consumption of the traction power supply system, has become a core issue that urgently needs to be addressed in the field of maglev train operation and scheduling.

[0006] From a control theory perspective, the train speed curve optimization problem involves solving the Hamilton-Jacobi-Bellman equations under spatially varying constraints. Existing research mainly employs three methodological paradigms: direct optimization, indirect optimal control, and dynamic programming.

[0007] Direct optimization methods transform the infinite-dimensional optimal control problem into a finite-dimensional optimization problem. By discretizing the state and control variables, the original infinite-dimensional problem is transformed into a standard nonlinear programming problem (Cheng et al., 2019; Jin et al., 2018). Xing et al. (2023) developed an improved brute-force search method to solve the multi-objective energy-saving problem in train operation, focusing on the utilization of regenerative braking energy. Wang et al. (2016, 2017) and Ye et al. (2016) used the pseudospectral method to study multi-stage speed curve optimization and multi-train control scheduling on railway lines. Zhou et al. (2024) applied a multibody dynamics model to reduce the influence of motion resistance by considering track conditions and cruising speed, thereby optimizing energy consumption.

[0008] Indirect optimal control methods are based on optimal control conditions, including the Pontryagin maximum principle and variational methods. These methods transform the optimization problem into an optimal control problem with analytically necessary conditions, deriving a set of two-point boundary value problems that satisfy the optimality conditions. Ichikawa (1968) first applied the Pontryagin maximum principle to solve bounded state variable problems. Howlett et al. (2009) explored optimal train control strategies considering various operational constraints based on the Pontryagin maximum principle. Albrecht et al. (2016a, 2016b) discussed the theoretical principles and computational techniques of optimal train control. Scheepmaker and Goverde et al. (2015) analyzed the trade-off between energy consumption and running time in train operation. However, indirect methods exhibit high computational complexity.

[0009] Dynamic programming provides a recursive framework for solving optimal control problems (Haahr et al., 2017; Lai et al., 2020). Dynamic programming combines elements of direct and indirect methods through a state-based decomposition strategy. It employs recursive decomposition and optimization, using the Bellman optimality principle to break down complex problems into manageable subproblems. Aredah et al. (2024) applied multi-objective dynamic programming to optimize freight train operation. Haahr et al. (2017) used dynamic programming to solve the speed curve optimization problem. Lai et al. (2020, 2024) used dynamic programming to solve the speed curve optimization problem for medium-speed maglev trains. However, dynamic programming is inherently limited to single-domain discretization schemes—either in the time domain or the spatial domain. This fundamental limitation stems from the recursive nature of dynamic programming, which requires the use of fixed independent variables for state transition calculations throughout the optimization process.

[0010] In existing technologies, research on train speed curve optimization mainly focuses on wheel-rail trains. Although some research involves maglev systems, maglev trains face multiple constraints during operation, such as dual-speed protection and passenger comfort, which significantly increases the difficulty of speed curve optimization. Furthermore, many optimization methods suffer from high computational complexity when dealing with the complex electrical and dynamic coupling relationships in maglev systems, making it difficult to meet real-time requirements. Therefore, existing methods still have significant shortcomings in comprehensively considering multiple constraints and achieving efficient optimization. There is an urgent need for an optimization method that can balance energy minimization and operational efficiency improvement under complex constraints to meet the diverse needs of actual operation. Summary of the Invention

[0011] The embodiments of the present invention provide a simulation optimization method for the operating speed curve of a maglev train based on virtual speed limit, which is used to solve the problems existing in the prior art.

[0012] To achieve the above objectives, the present invention adopts the following technical solution.

[0013] A simulation optimization method for the operating speed curve of maglev trains based on virtual speed limits includes: S1 describes the operation process and electrical characteristics of the maglev train by constructing a discrete state-space model; S2 describes the operation process and electrical characteristics of the maglev train based on the discrete state-space model, and calculates all states of the maglev train operation process through the transformation function. S3 calculates the initial speed curve based on all states of the maglev train operation process through a mapping function; S4 simulates the maglev train operation through a spatiotemporal hybrid adaptive speed curve simulation method based on all states and the initial speed curve of the maglev train operation process, and adjusts the speed of the maglev train through a virtual speed limit generation mechanism, so that the optimal speed curve of the maglev train operation process can be obtained after the maglev train operation simulation process. The optimal speed curve during the operation of a maglev train is used for the control optimization of the maglev train.

[0014] Preferably, step S1 includes: Through

[0015] Construct a discrete state-space model; where: Position status (meters); Speed ​​status (m / s); Time status (seconds); The cumulative energy consumption state (kilowatt-hours) represents the total energy consumption from the starting point to the current state point; This represents the q-axis current state (Amperes), used for voltage calculation and tracking current changes; To ensure a uniform traction and braking coefficient, the range is from -1 to 1, with positive values ​​representing traction force, negative values ​​representing braking force, and zero representing no force that can be applied. Let be the operating mode state vector, representing the vehicle's operating state at the end of the i-th simulation step; in the operating mode state vector, the traction variable Capture traction dynamics, where -1 represents the traction coefficient. The value decreases from the current value to 0, where 0 indicates no traction and 1 indicates that the traction coefficient increases from the current value to 1; cruise variable. It's binary; 0 indicates non-cruise mode, and 1 indicates constant speed cruise mode. Lazy variable. Distinguish between non-coasting state 0 and coasting state 1. In coasting state, the vehicle moves under inertia without power input; braking variable. Capture braking dynamics, where -1 represents the braking coefficient. The value decreases from the current value to 0, where 0 indicates no braking and 1 indicates that the braking coefficient increases towards -1.

[0016] Preferably, step S2 includes: By transforming the functional expression

[0017] The train state transition values ​​are calculated, and the operation process of the maglev train is described by these values; where: Indicates the first i The interval is the first r and the r Maximum speed limit at position +1 The constraint set includes electrical parameter constraints, maximum speed limit constraints, acceleration impact rate limits, boundary state constraints, and dual-speed protection constraints; the constraint set is expressed as follows:

[0018] Calculated; where: These represent electrical parameter constraints, including upper limits for q-axis current, q-axis voltage, and active power, which are derived from the rated capacity of traction substations and transmission facilities. This represents the maximum speed limit constraint, ensuring that the train speed does not exceed the virtual speed limit of the current zone; This represents the acceleration impact rate limit, used to ensure passenger comfort by limiting the rate of change of acceleration to no more than a preset threshold. Represents boundary state constraints, specifying the velocity, position, and time conditions for the start and end points; This represents dual-speed protection constraints, including requirements for emergency braking safety distance and loss-of-power coasting distance.

[0019] Preferably, step S3 includes: S31 via mapping function expression

[0020] Calculate the next speed of the maglev train in traction mode. And the speed at which the maglev train reaches the next speed-limited zone in coasting mode. ; S32 If Then the maglev train is controlled to be in traction mode. ;like If so, the maglev train will be in cruise mode; if Then the maglev train is controlled to be in coasting mode. ;like Then the maglev train is controlled to be in braking mode. ; S33 Based on the maglev train operation mode judgment result obtained in sub-step S32, the formula is used...

[0021] Update the traction and braking coefficients of the maglev train; where: It is a velocity-dependent single-step change, determined by the maximum acceleration impact rate constraint; It is the dot product of the operating mode vector and the direction control vector; the direction control vector The sign of each component is determined based on the current traction coefficient value and operating mode status of the maglev train, specifically through a combination of the following four sub-functions:

[0022] Of the four functions mentioned above: Defined as the control function for traction mode, when When this time, it indicates that traction needs to be increased, and the vehicle should return. If the absolute value of the current coefficient is less than 1, then return a positive value. Increase; if it has reached 1, return to zero and remain unchanged; when When this is the case, it indicates that the traction force needs to be reduced and the vehicle needs to return. ,in It is an indicator function, in When it is 1, it is 0 when it is equal to 0, ensuring Decrease toward zero; when When the time indicates a non-traction state, returning to zero makes It does not change with the traction mode; Defined as the control function for cruise mode, when When, return ,drive To threshold Approach; It is the balance coefficient required for cruising, ensuring that traction equals drag; through gradual adjustment to ; The control function defined as lazy mode, when When, return ,drive Decrease toward zero; Defined as the control function for braking mode, when When, return ,make Increasing towards -1 increases braking force; when When, return This reduces the braking force until it reaches zero. S34 Through-type

[0023] The resultant force acting on the maglev train is calculated; where: The updated traction coefficient; The maximum traction force is dependent on position and speed.

[0024] Preferably, step S4 includes: S41 Through Type

[0025] Calculate the slope of the initial position state at a given time step. ; Through

[0026] Calculate the slope of the velocity state at this initial point. In the formula: It is the current traction or braking force. and These are the basic resistance and the line resistance, respectively. It's about train quality; Through

[0027] Calculate the slope of the energy consumption state at this initial point. ; Through

[0028] Calculate the slope of the q-axis current state at this initial point. ; S42 Slope based on the initial point's position state The slope of the velocity state Slope of energy consumption state and the slope of the q-axis current state The slopes of the remaining position states are calculated using the RK4 method. The slope of the velocity state Slope of energy consumption state and the slope of the current state ; S43 Slope based on all position states The slope of the velocity state Slope of energy consumption state and the slope of the current state , through

[0029] The operating status of the maglev train is updated by weighting and combining the four slopes. S44 uses a verification feedback mechanism.

[0030] Determine whether the change in the operating state of the maglev train obtained in sub-execution step S43 is within the preset acceptable range. If so, repeat sub-steps S41 to S44 to calculate the operating state of the maglev train for the next time step. Otherwise, determine that the maglev train is in a high-speed operating state and execute sub-step S45. S45 Through-type

[0031] The high-speed operating status of the maglev train is updated, and the spatial resolution is improved; where the slope of the position state is... The slope of the velocity state Slope of energy consumption state The slope of the current state The slope of the velocity state and the slope of the time state Obtained by the RK4 method.

[0032] Preferably, in step S3, the following constraints are added during each transition of the maglev train's operating state: Electrical parameter constraints, the conditional expression is:

[0033] Passenger comfort constraints, including the following conditions: Formula for calculating acceleration impact rate

[0034] Conditional expression for the change of single-step traction coefficient in time-domain discretization

[0035] Conditional expression for the change of single-step traction coefficient in spatial discretization

[0036] Dual-velocity protection constraints, the conditional expressions include: Inverse dynamic equations of the braking process

[0037] Dynamic equations of unpowered gliding

[0038] Glide distance constraints

[0039] Speed ​​limit inflection point constraint, the condition is as follows: .

[0040] Preferably, in step S4, the process of adjusting the speed of the maglev train through the virtual speed limit generation mechanism includes: The maglev line is divided into R virtual speed-limited zones, each with a length of... Number of partitions Based on the total length of the line and partition length Decision, satisfaction In the formula, Indicates rounding up; Through

[0041] Calculate and obtain virtual speed limit vectors for various operating conditions. ; Various operating conditions include: The maximum speed limit of the current partition is higher than that of the next partition. And it's not the first partition. ; The current partition has the same maximum speed limit as the previous partition. And it is in the intra-block cruise segment ; The current partition has the same maximum speed limit as the previous partition. And it is in the decreasing segment within the block. ; The maximum speed limit of the current partition is lower than that of the next partition. This indicates that you have entered a region with an increased speed limit. Set candidate solutions The virtual rate limit generation mechanism is invoked to generate a complete virtual rate limit configuration. ; The virtual speed limit configuration and fixed line vehicle parameters are input into the maglev train operation simulation process for calculation, so that the maglev train operation simulation process can simulate the train's operation process from the starting point to the destination according to the virtual speed limit and line conditions, generate detailed speed curves, and record the position, speed, running time, and energy consumption information of each state point. Extract runtime from the information of each recorded state point. and energy consumption ;, through formula

[0042] Construct an objective function, and obtain candidate solutions by solving the objective function; where: It is a predefined runtime requirement. It is a weighting factor for runtime deviation, used to reflect the importance of on-time performance. It is the weighting coefficient for energy consumption; Determine whether the candidate solutions obtained by solving the objective function are infeasible; if so, return a maximal value of the objective function. And obtain the value sequence of the objective function. ; Based on the value sequence of the objective function, the first... generation Sort the nth candidate solution in ascending order to obtain an ordered sequence of solutions. Let the sorted nth solution be denoted as . The solution is ,in It is a sorting and permutation function that satisfies ; Through

[0043] Select the first sorted items Each solution is considered as the set of optimal solutions; where... It is the optimal solution retention ratio parameter; Extract candidate solutions from the optimal solution set. All A virtual speed limit block ; Through

[0044] Perform a random reorganization decision on a given virtual speed limit block, generating a uniformly distributed random number. And compare it with the threshold of 0.5: If Then retain the virtual speed limit block at the current position. Unchanged; otherwise, through formula

[0045] Replace the virtual speed limit block at the current position with the virtual speed limit block at the next position. Obtain the recombined virtual speed limit block sequence

[0046] Through

[0047] For a certain virtual speed limit block after reorganization Update; where: It is the number of partitions within a certain reorganized virtual rate-limiting block; These are global control parameters; Through

[0048] Generate a new virtual speed limit sequence to replace the recombined virtual speed limit block. ,get A new candidate solution is found, and the new candidate solution set is used.

[0049] Express; Through

[0050] Merge the new set of candidate solutions; Based on the merged solution Repeat step S4 based on the maximum number of iterations G to obtain the combined solution after multiple rounds; Through

[0051] After multiple rounds of merging, the solution with the smallest objective function value is selected as the optimal solution.

[0052] As can be seen from the technical solutions provided by the embodiments of the present invention above, the present invention provides a simulation optimization method for the operating speed curve of maglev trains based on virtual speed limits. It proposes a spatiotemporal hybrid adaptive discretization method, which can dynamically switch between time and spatial domain calculation modes according to train speed. This ensures time resolution at low speeds and maintains spatial resolution at high speeds, fundamentally eliminating the speed-dependent errors caused by single-domain methods and achieving consistent numerical accuracy across the entire speed domain. Furthermore, the present invention introduces virtual speed limits as a core decision variable, transforming the complex high-dimensional continuous control problem into a structured discrete input sequence problem. By adjusting the distribution of virtual speed limits, indirect control of traction, cruise, coasting, and braking processes is achieved, significantly reducing the optimization dimensionality. Combined with a virtual speed limit block partitioning mechanism and embedded constraint processing strategy, this method can automatically generate physically feasible optimal speed curves under multiple constraints, including dual-speed protection, safe braking distance, and passenger comfort. Compared with existing technologies, the present invention, while ensuring safety and comfort, achieves a significant reduction in operating energy consumption and a substantial improvement in computational efficiency, providing a more accurate, efficient, and engineering-feasible solution for optimizing the speed curve of maglev trains.

[0053] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0054] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 The flowchart of the simulation optimization method for the operating speed curve of a maglev train based on virtual speed limit provided by the present invention is shown below. Figure 2 The logic block diagram of the simulation optimization method for the operating speed curve of a maglev train based on virtual speed limit provided by the present invention; Figure 3 This is a schematic diagram of the virtual speed limit partitioning structure and block division of the maglev train speed curve simulation optimization method based on virtual speed limit provided by the present invention. Detailed Implementation

[0056] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0057] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0058] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0059] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0060] This invention provides a simulation optimization method for the operating speed curve of a maglev train based on virtual speed limits, which addresses the following technical problems existing in the prior art: Currently, research on train speed curve optimization mainly focuses on the operating speed optimization of wheel-rail trains, although some research also involves maglev systems. However, existing optimization methods face significant difficulties in solving the multiple constraints encountered during maglev train operation, such as dual-speed protection and passenger comfort. Specifically: Limitations of analytical methods: Analytical methods are typically based on optimal control theory, transforming the speed curve optimization problem into a two-point boundary value problem. While a relatively simple optimal trajectory can be derived in traditional wheel-rail systems by simplifying the resistance and traction force models, in maglev systems, the complex electrical model of the long-stator linear motor, the dual-end power supply mode, and levitation energy consumption make analytical methods difficult to apply to the speed curve optimization of maglev trains. Analytical methods cannot effectively handle position-dependent motor impedance variations in maglev systems. These variations create spatially heterogeneous energy conversion patterns along the track, rendering traditional analytical solution methods ineffective.

[0061] The computational bottleneck of numerical methods: Numerical methods such as mixed-integer programming and dynamic programming discretize the infinite-dimensional optimal control problem into a finite-dimensional optimization problem. Although applicable to speed optimization of medium-speed maglev trains, the state space expands dramatically under high-precision speed and spatial discretization constraints, as well as multiple safety and comfort constraints. This leads to a significant increase in computation time and resource consumption, making it difficult to meet the real-time requirements of actual operation. Furthermore, although these methods can theoretically find relatively accurate optimal solutions, their high computational complexity and time cost limit their application in real-time scheduling and large-scale systems.

[0062] The inherent limitations of single-domain discretization: Existing dynamic programming methods are inherently limited to single-domain discretization schemes, i.e., either time-domain discretization or spatial-domain discretization. In time-domain discretization, the fixed time step causes the spatial increment to become a function of velocity. As the velocity increases, the spatial interval becomes larger, leading to insufficient spatial sampling and an inability to capture crucial positional information and electromagnetic variations along the track. Conversely, in spatial-domain discretization, the fixed spatial step generates velocity-dependent time increments. As the velocity decreases, the time interval increases, failing to adequately analyze transient dynamic characteristics and rapid electromagnetic coupling effects. When solving coupled multivariable nonlinear differential equation systems, this single-domain discretization strategy inevitably introduces velocity-dependent discretization errors due to the need to apply linear approximations at each discretization step, resulting in fluctuations in computational accuracy across different velocity ranges.

[0063] The decision variables are too high-dimensional: Existing studies typically use train status as the decision variable, including speed, acceleration, traction / braking force, and current. However, directly optimizing these high-dimensional continuous variables is computationally forbidden for maglev systems because the position-dependent motor characteristics and complex spatiotemporal constraints create intricate interdependencies among these variables.

[0064] To address the aforementioned shortcomings, this invention aims to develop a speed curve optimization method for maglev trains that can simultaneously minimize energy consumption and improve operational efficiency under complex constraints. Specific objectives include: This invention comprehensively considers multiple constraints, including dual-speed protection and passenger comfort, during the optimization process to ensure that the optimized result not only has energy consumption advantages but also meets safety and ride comfort requirements. By continuously evaluating the compliance of the dual-speed protection constraints during simulation, this invention eliminates the need to explicitly incorporate these constraints as input parameters.

[0065] Reducing computational complexity: By introducing a "virtual speed limit" as a key decision variable, the continuous high-dimensional speed control problem is transformed into a structured discrete input sequence problem, significantly reducing the complexity of the solution space while retaining the basic characteristics of the optimal driving strategy. This invention organizes speed limits into coherent blocks based on track characteristics and employs hierarchical partitioning, significantly reducing the dimensionality of the feasible solution search space while maintaining solution quality.

[0066] Addressing the discretization error problem: A spatiotemporal hybrid adaptive discretization method is developed, dynamically switching between time-based and distance-based simulation steps to ensure computational accuracy in different velocity domains while characterizing position-dependent impedance variations. This method specifically addresses the fundamental limitation of single-domain discretization methods, namely, the velocity-dependent approximation error that arises when applying linear approximations to solve inherently nonlinear multivariable ordinary differential equation systems.

[0067] Improving Optimization Accuracy and Efficiency: This invention utilizes simulation methods to model the electrical and power conversion relationships during maglev train operation. Combined with flexible adjustments to virtual speed limits, it generates variable speed curves that meet the requirements of actual lines, achieving dual optimization of energy consumption and operating time. Compared to existing methods, this invention significantly improves solution efficiency while maintaining high accuracy, making the speed curve optimization process more efficient and energy-saving, greatly enhancing the economy and sustainability of maglev train operation.

[0068] See Figure 1 This invention provides a simulation optimization method for the operating speed curve of a maglev train based on virtual speed limits, comprising the following steps: S1 describes the operation process and electrical characteristics of the maglev train by constructing a discrete state-space model; S2 describes the operation process and electrical characteristics of the maglev train based on the discrete state-space model, and calculates all states of the maglev train operation process through the transformation function. S3 Based on all states of the maglev train operation, the initial speed curve is calculated through a mapping function; S4 Based on all states of the maglev train operation and the initial speed curve, the maglev train operation simulation is performed through a spatiotemporal hybrid adaptive speed curve simulation method, and the speed of the maglev train is adjusted through a virtual speed limit generation mechanism, so that the optimal speed curve of the maglev train operation can be obtained after the maglev train operation simulation process.

[0069] The optimal speed curve during the operation of a maglev train is used for the control optimization of the maglev train.

[0070] This invention proposes a simulation-based method for optimizing the speed curve of maglev trains. This method addresses the position-dependent characteristics of the long-stator linear synchronous motor, multiple nonlinear spatiotemporal constraints, and complex electro-dynamic coupling relationships during maglev train operation, constructing a complete optimization technology system. The core idea of ​​this method is to transform the high-dimensional continuous control problem, which is difficult to handle in existing optimization methods, into a structured discrete input sequence problem. By introducing a virtual speed limit as a decision variable and combining it with a high-precision hybrid spatiotemporal domain simulation algorithm, the method achieves a balance between minimizing energy consumption and meeting operating time constraints within an iterative optimization framework.

[0071] The entire technical solution consists of three core components: a spatiotemporal hybrid maglev train speed curve simulation algorithm, a virtual speed limit generation mechanism, and an iterative optimization process. The spatiotemporal hybrid maglev train speed curve simulation algorithm, acting as the execution engine, is responsible for transforming the given virtual speed limit configuration into a detailed speed curve and accurately calculating the running time and energy consumption. Then, the train's traction control is adjusted using the optimal speed curve to achieve optimal energy consumption. The algorithm's innovation lies in employing a spatiotemporal hybrid adaptive discretization method, dynamically selecting the time or spatial domain discretization scheme based on the train speed. This eliminates the speed dependence error of single-domain discretization methods, ensuring accurate numerical solutions for position-dependent motor characteristics and coupled dynamic systems across the entire speed domain. The virtual speed limit generation mechanism, acting as a decision variable manager, generates and updates the virtual speed limit configuration, significantly reducing the dimensionality and complexity of the optimization problem. The iterative optimization process, through a closed-loop feedback mechanism of evaluation, selection, and updating, drives the virtual speed limit configuration to converge towards the optimal solution.

[0072] like Figure 1As shown, the three core components form a complete optimization closed loop through standardized data interfaces. The virtual speed limit generation mechanism generates an initial candidate solution set based on line characteristics and optimization requirements, with each candidate solution representing a complete set of virtual speed limit configurations. The spatiotemporal hybrid maglev train speed curve simulation algorithm receives the virtual speed limit configurations and fixed line and vehicle parameters, and outputs speed curves, running time, and energy consumption data through simulation. The iterative optimization process selects high-quality solutions based on the objective function evaluation results and generates a new generation of candidate solutions through block recombination and block update mechanisms, feeding the improved virtual speed limit configurations back to the simulation algorithm for the next round of evaluation. This closed-loop architecture realizes a continuous improvement process of "decision variable generation → accurate simulation evaluation → fitness-oriented update → convergence to the optimal solution," systematically minimizing the energy consumption of the traction power supply system while satisfying multiple operational constraints.

[0073] Figure 1 This paper presents the overall technical architecture of the simulation-based speed curve optimization method for maglev trains based on this invention. The architecture employs a closed-loop design and consists of three interdependent core components. The spatiotemporal hybrid maglev train speed curve simulation algorithm, located at the center of the architecture, acts as the execution engine. It receives virtual speed limit configurations as input and generates a complete speed curve that meets the requirements of the actual line by simulating the electrical, power, and motion state transitions of the train under different operating conditions. Internally, the algorithm includes state transition logic, a hybrid adaptive discretization switching mechanism, and a constraint checking module to ensure high accuracy and physical feasibility of the simulation process. The virtual speed limit generation mechanism is responsible for generating and managing decision variables. This mechanism first divides the line into virtual speed limit blocks based on the maximum speed limit distribution, dividing the line into several virtual speed limit blocks, each containing consecutive partitions with the same maximum speed limit. Then, according to the virtual speed limit generation mechanism, a virtual speed limit value is determined for each partition, forming a complete virtual speed limit vector. Through randomized cruise intervals and a stepped speed reduction design, this mechanism can systematically generate diverse candidate virtual speed limit configurations, significantly reducing the dimensionality of the solution space. The iterative optimization process, located on the right side of the architecture, acts as a strategic coordinator driving the entire optimization process. The process includes key steps such as fitness evaluation, solution selection, block reorganization, block update, and generation of a new generation of solutions. Through a optimal solution retention strategy and an adaptive update probability mechanism, the iterative optimization process maintains solution diversity while continuously converging towards the optimal direction of the objective function. Information is exchanged between the three components through a clear data flow: the virtual rate limit generation mechanism provides candidate virtual rate limit configurations to the simulation algorithm; the simulation algorithm feeds back runtime and energy consumption data to the iterative optimization process; and the iterative optimization process guides the virtual rate limit generation mechanism to generate improved configurations based on the evaluation results. The entire architecture forms a closed-loop system of continuous feedback and adaptive improvement, ultimately outputting the optimal speed curve that minimizes energy consumption and meets runtime requirements.

[0074] (1) Simulation algorithm for speed curve of hybrid maglev train in spatiotemporal domain

[0075] The spatiotemporal hybrid maglev train speed curve simulation algorithm is the core execution module of this invention. Its main function is to transform the input virtual speed limit configuration into a detailed train speed curve, while simultaneously calculating key performance indicators such as running time and energy consumption. The algorithm's design fully considers the unique characteristics of the maglev system, including the position-dependent characteristics of the long-stator linear synchronous motor, the switching between single-end and dual-end power supply modes, dual-speed protection requirements, and passenger comfort constraints. By employing a discrete state-space model to describe the train's operation, the algorithm can accurately characterize the train's position, speed, time, energy consumption, current, and operating mode at each simulation step, providing an accurate data foundation for subsequent energy consumption calculations and optimization decisions.

[0076] The algorithm's technological innovations are mainly reflected in three aspects: First, it establishes a complete system state definition framework, comprehensively describing the train's operating state and electrical characteristics through multi-dimensional state vectors; second, it designs a state transition method based on optimal driving strategies, automatically determining the train's operating mode according to changes in virtual speed limits; and most importantly, it proposes a spatiotemporal hybrid adaptive discretization method, dynamically selecting the discretization scheme based on train speed, fundamentally solving the speed-dependent error problem of single-domain discretization methods. These three technical elements work together to form a high-precision, high-efficiency simulation system, providing a reliable evaluation tool for speed curve optimization.

[0077] System state definition

[0078] This invention employs a discrete state-space model to describe the operation of a maglev train. This modeling method effectively controls computational complexity while ensuring computational accuracy. The system state is completely recorded at the end of each simulation step, forming a sequence of state points. Connecting these state points constitutes the train's speed curve and the trajectory of related physical quantity changes. The maglev train simulation system uses a discrete state-space model, with each state point... It includes the following key elements:

[0079] in: Position status (meters); Speed ​​status (m / s); Time status (seconds); The cumulative energy consumption state (kilowatt-hours) represents the total energy consumption from the starting point to the current state point; This represents the q-axis current state (Amperes), used for voltage calculation and tracking current changes; The operating mode state vector represents the operating state of the vehicle at the end of the i-th simulation step; To unify the traction and braking coefficient states, the range is from -1 to 1, with positive values ​​representing traction force, negative values ​​representing braking force, and zero representing no force that can be applied.

[0080] In the operating mode state vector, the traction variable Capture traction dynamics, where -1 represents the traction coefficient. The value decreases from the current value to 0, where 0 indicates no traction and 1 indicates the traction coefficient increases from the current value to 1. Cruise variable. It's binary; 0 indicates non-cruise mode, and 1 indicates constant speed cruise mode. Lazy variable. Distinguish between non-coasting state 0 and coasting state 1. In coasting state, the vehicle moves due to inertia without power input. Braking variable. Capture braking dynamics, where -1 represents the braking coefficient. The value decreases from the current value to 0, where 0 indicates no braking and 1 indicates that the braking coefficient increases towards -1.

[0081] Through the complete definition of the above seven state variables, this invention establishes a comprehensive and accurate train operation state description system. This state-space model not only encompasses kinematic and dynamic information (position, velocity, time), but also includes electrical system information (current, energy consumption) and control logic information (operation mode, traction coefficient), enabling a complete characterization of the physical and control characteristics of the maglev train during operation. During simulation, the state vector is updated at each discrete step, mapping from the current state to the next state through a state transition function, progressively advancing the simulation process. The generation of the state sequence is essentially a numerical solution process of the maglev system's dynamic equations under multiple constraints, and the resulting state trajectory represents the train operation process under a given virtual speed limit configuration.

[0082] State transition method

[0083] The state transition method is the core logic of the simulation algorithm, defining how the system state evolves from one moment to the next. In the discrete-event dynamic system of this invention, state transitions are controlled by a comprehensive transition function. This function determines the next state based on the current state and external input (virtual speed limit), while satisfying all operational constraints. The mathematical expression of the state transition function is:

[0084] in Indicates the first i The interval is the first r and the r Maximum speed limit at position +1 It is a set of constraints, including electrical parameter constraints, maximum speed limit constraints, acceleration impact rate limits, boundary state constraints, and dual-speed protection constraints.

[0085] Constraint Set It is a key element in ensuring the physical feasibility and operational safety of simulation results, and it is defined as a set of five types of constraints:

[0086] in, These represent electrical parameter constraints, including upper limits for q-axis current, q-axis voltage, and active power, which are derived from the rated capacity of traction substations and transmission facilities. This represents the maximum speed limit constraint, ensuring that the train speed does not exceed the virtual speed limit of the current zone. This represents the acceleration impact rate limit, used to ensure passenger comfort by limiting the rate of change of acceleration to no more than a preset threshold. Represents boundary state constraints, specifying the velocity, position, and time conditions of the starting and ending points. This represents dual-speed protection constraints, including requirements for emergency braking safety distance and slip distance in the event of power loss, and is a unique safety protection mechanism for maglev systems.

[0087] The core logic of the state transition is based on the optimal driving strategy theory, which states that the energy-optimal train operation process typically follows a "maximum power—cruising—coasting—maximum braking" pattern. Based on this principle and considering the characteristics of virtual speed limits, this invention designs a mapping mechanism for automatically determining the operating mode. The input to this mechanism is the maximum speed limit value of two consecutive virtual speed limit zones, and the output is the corresponding operating mode state. The specific mapping relationship is defined by a function... definition:

[0088] The design of this mapping function follows the following logical principle: The current and subsequent virtual speed limit partitions satisfy... When the system is in a relationship with a speed limit increase or decrease, it indicates that the train has entered a section where the speed limit is either increased or maintained. In this case, the system prioritizes either traction or cruise mode to increase speed or maintain high-speed operation. The specific criterion is to predict the speed of the next step in traction mode. ,like This indicates that even with traction applied, the current speed limit will not be exceeded; therefore, traction mode should be selected. ;like This indicates that continuing to tow will lead to speeding; at this point, switch to cruise control. By adjusting the traction coefficient, the traction force and resistance are balanced to maintain constant speed operation.

[0089] Conversely, when When this occurs, it indicates that the speed limit ahead has been lowered, and the train needs to slow down to meet the new speed limit requirements. At this point, the system needs to determine whether to use coasting or braking to achieve deceleration. The criterion is the predicted speed when reaching the next speed-limited zone in coasting mode. ,like This indicates that the next speed limit requirement can be met simply by coasting (naturally decelerating under resistance), in which case coasting mode should be selected. To save energy; if This indicates insufficient deceleration during coasting, and braking force must be applied. In this case, select the braking mode. This forward-looking prediction-based mode selection strategy embodies the core idea of ​​optimal driving theory: while meeting speed limits, minimize braking and prioritize coasting for deceleration to reduce energy consumption.

[0090] After determining the operating mode status, the traction and braking coefficients need to be updated according to the mode. The coefficients are updated according to the following rules:

[0091] In this updated formula, It is a speed-dependent single-step change, the magnitude of which is determined by the maximum acceleration impact rate constraint to ensure that the rate of change of acceleration does not exceed the allowable value, thereby ensuring passenger comfort. It is the dot product of the operation mode vector and the direction control vector. Due to the mutual exclusivity of the operation mode variables, the result of this dot product is a scalar, indicating... Should it be increased, decreased, or kept unchanged? Direction control vector. The sign of each component is determined based on the current traction coefficient value and operating mode status, specifically defined as a combination of four sub-functions:

[0092] traction mode control function Defined as follows: when When this time, it indicates that traction needs to be increased, and the vehicle should return. If the absolute value of the current coefficient is less than 1, then return a positive value. Increase; if it has reached 1, return to zero and remain unchanged; when When this is the case, it indicates that the traction force needs to be reduced and the vehicle needs to return. ,in It is an indicator function, in When it is 1, it is 0 when it is equal to 0, ensuring Decrease toward zero; when When the time indicates a non-traction state, returning to zero makes It does not change with the traction mode.

[0093] Cruise mode control function Defined as follows: when When, return ,drive To threshold Move closer. Here. It is the balance coefficient required for cruising, ensuring that traction is exactly equal to drag. This is achieved through gradual adjustments. to This enabled a smooth transition to cruise mode.

[0094] Lazy mode control function Defined as follows: when When, return ,drive Decrease towards zero to eventually achieve coasting.

[0095] Braking mode control function Defined as follows: when When, return ,make Increase towards -1 (note the negative value corresponding to braking) to increase braking force; when When, return This reduces the braking force until it reaches zero.

[0096] Through the above coefficient update mechanism, the system can automatically and smoothly adjust the magnitude of traction or braking force according to the current operating mode and status, ensuring that the force application process conforms to the acceleration impact rate constraint and avoiding sudden changes that may cause discomfort to passengers. Updated traction coefficient Maximum traction force dependent on position and speed Combined, the resultant force acting on the train can be calculated:

[0097] This resultant force will be used to solve the next step of the dynamic equations, driving the evolution of the train's state. It is important to emphasize that... The position-dependent characteristics stem from the structural features of long-stator linear synchronous motors: the stator segment length may vary at different positions, and the switching between single-ended and dual-ended power supply modes in different sections causes the motor's electrical impedance to change with position, thus affecting the maximum output force. The speed-dependent characteristics arise from the laws of electromagnetic induction and power limitations: at low speeds, it is limited by current, and at high speeds, by voltage or power limitations, forming typical constant torque and constant power regions. This invention ensures that the simulation results accurately reflect the actual operating characteristics of the maglev system by accurately modeling these position and speed dependencies.

[0098] The design of the state transition method fully demonstrates the invention's profound understanding of the characteristics of maglev systems and its effective application of optimal driving strategies. By mapping the relationship between two consecutive virtual speed limits to an operating mode, and then controlling the evolution of the traction coefficient through the operating mode, the entire logical chain is clearly and logically defined, ultimately transforming it into a force that drives the dynamic equations. This design not only simplifies the complexity of control decisions but also automatically generates speed curves that conform to optimal driving principles, laying a solid foundation for subsequent energy consumption optimization.

[0099] Spatiotemporal hybrid adaptive discretization method

[0100] The spatiotemporal hybrid adaptive discretization method is one of the most important technical innovations of this invention. It fundamentally solves the velocity-dependent error problem existing in the single-domain discretization method when solving the dynamic equations of the maglev system. The operation of a maglev train is essentially a spatiotemporally coupled physical system, and its state evolution... Simultaneously dependent on speed and location The system is governed by a set of coupled multivariable nonlinear ordinary differential equations, in which velocity and position exhibit a strong interdependence. Numerical solutions to these equations require discretization of time or space, transforming a continuous problem into a discrete computation. However, traditional methods employ a single discretization domain (either a fixed time step or a fixed spatial step), which introduces velocity-varying discretization errors when applying linear approximations to solve inherently nonlinear systems.

[0101] Specifically, in the time-domain discretization method, a fixed time step is used. Numerical integration is performed. Within each time step, the system assumes that the changes in the state variables can be approximated by linear or low-order polynomials. However, the train's displacement... It is a function of speed; as speed increases, the spatial distance traversed per unit time increases. At high speeds, a fixed time step may result in a single step covering distances of tens or even hundreds of meters, while key characteristics of the maglev system, such as stator parameters and power supply modes, vary spatially. This insufficient spatial sampling leads to an inability to accurately capture position-dependent electromagnetic characteristic changes; for example, it may miss a short stator segment or a power supply mode switching point, thus introducing significant calculation errors. This is especially true when calculating position-dependent resistance. ,inductance and maximum traction Insufficient spatial resolution can cause changes in these parameters to be ignored, ultimately affecting the accuracy of energy consumption calculations.

[0102] Conversely, in spatial domain discretization methods, a fixed spatial step size is used. Numerical integration is then performed. At this point, the system uses position as the independent variable and velocity, time, etc., as dependent variables, and the dynamic equations are re-expressed in a form with position as the parameter. Within each spatial step, the time increment... It becomes a function of speed. When speed decreases, it takes longer to travel the same spatial distance; the time interval increases. At low speeds, this excessively large time interval leads to insufficient time resolution, making it impossible to accurately characterize rapidly changing transient dynamic characteristics. For example, during acceleration or braking, the traction coefficient... q-axis current These parameters can change rapidly over a short period of time. If the time step is too large, these rapid changes will be underestimated, leading to inaccurate modeling of electromagnetic coupling effects. Furthermore, at extremely low speeds (such as during startup or shutdown), the time step of spatial domain discretization can become extremely large, even causing numerical instability.

[0103] This hybrid approach is designed based on an important physical insight: the switching criterion. This actually represents the optimal balance point for the two discretization schemes to achieve equivalent resolution characteristics. At this point, the single-step spatial span of the time-domain discretization is exactly equal to the spatial step size of the spatial-domain discretization, and the discretization error characteristics of the two schemes for nonlinear differential equation systems are comparable. Any deviation from this balance point will lead to an increase in the error of one of the schemes. By dynamically switching the discretization domain at the balance point, the hybrid method ensures that the spatiotemporal resolution remains at or near-optimal levels throughout the entire velocity range.

[0104] The specific implementation of the spatiotemporal domain hybrid adaptive discretization method comprises three tightly integrated components: time-domain discretization computation, a verification feedback mechanism, and spatial-domain discretization computation. These three components together constitute an adaptive numerical integration framework.

[0105] The time-domain discretization method is the preferred computational mode for hybrid frames, suitable for low to medium speed ranges. In this method, time is the independent variable, and the state vector... The components evolve over time. Given a fixed time step... (Typically 1.0 second) Numerical integration is performed using the fourth-order Runge-Kutta (RK4) method. The RK4 method is a classic high-precision explicit integration method that achieves fourth-order accuracy (error order 1) by calculating four intermediate slopes and taking a weighted average. (This method) has much higher accuracy than the Euler method or second-order method at the same time length.

[0106] The first step of the RK4 method is to calculate the slope of the initial point. For the position state, the slope is the current velocity. For the velocity state, the slope is given by Newton's second law. ,in It is the current traction or braking force. and These are the basic resistance and the line resistance, respectively. It represents the train's mass; for energy consumption conditions, the slope is the instantaneous total power. This includes traction power and levitation power; for the q-axis current state, the slope is the rate of change of current. It is calculated based on the electrical equations of the motor.

[0107] The second step is to calculate the slope at the midpoint of the time step. First, according to Midpoint State Estimation: Position Advancement Speed ​​increases Then estimate the midpoint state after advancement. Recalculate the physical quantities and slopes. The third step is similar, but uses... Estimate the state of the other midpoint and calculate the result. Step 4 uses Estimate the state at the end of the time step and calculate Finally, the state update is obtained by weighting the four slopes:

[0108] This weighted averaging method effectively cancels out low-order error terms, reducing single-step error to a fifth-order small quantity and greatly improving computational accuracy.

[0109] The validation feedback mechanism is the core of the hybrid method's decision-making process, responsible for determining whether the time-domain results are acceptable. After each time-domain discretization calculation, the system immediately evaluates the change in position during the calculation. and with the preset spatial step size threshold Comparison:

[0110] If this condition is met, it indicates that the spatial span of the current time step is within an acceptable range, the spatial resolution is sufficient, and the time-domain discretization result is acceptable. The simulation can then continue using the time-domain method for the next step. If this condition is not met, it indicates that due to the high speed, the fixed time step results in an excessively large spatial distance spanned in a single step, exceeding the threshold, which may prevent accurate capture of changes in position-dependent characteristics. In this case, the system determines that it needs to switch to spatial domain discretization to improve spatial resolution.

[0111] This verification feedback mechanism embodies the principles of adaptive computing. Unlike hard switching based on speed, the feedback mechanism dynamically determines the threshold based on the actual computation results, offering greater flexibility. Typically, a value of around 25 meters is chosen. The selection of this value requires a balance between computational efficiency and accuracy: too small a value leads to frequent switching, while too large a value makes it impossible to effectively control spatial resolution. In practical applications, this threshold can be determined based on factors such as the typical length of the stator segment on the line and the spacing between power supply zones, ensuring that important spatial characteristic changes are not missed.

[0112] The spatial domain discretization method is activated when the verification feedback mechanism determines that a switch is needed, and is suitable for high-speed segments. In this method, position... The time-space variable becomes the independent variable, while other state variables evolve with position as dependent variables. The dynamic equations require variable substitution, converting the time derivative to the spatial derivative. Using the chain rule, we have:

[0113] Therefore, the derivative of velocity with respect to time can be converted into its derivative with respect to position:

[0114] Similarly, the derivatives of the other state variables with respect to position are:

[0115] Based on these transformed differential equations, numerical integration is also performed using the RK4 method, but this time the spatial step size is fixed. The calculation process is similar to that in the time domain, calculating the four slopes sequentially. The only difference is that the independent variable changes from time to position. The final state update formula is:

[0116] The advantage of spatial domain discretization is that, regardless of velocity changes, the spatial span of each step is fixed, enabling uniform sampling of position-dependent physical quantities and accurately capturing the spatial variation characteristics of stator segment parameters, power supply modes, etc. In the high-speed range, due to the high speed, the corresponding time increment automatically decreases. This provides sufficient time resolution.

[0117] The spatiotemporal domain hybrid adaptive discretization method achieves the goal of automatically selecting the optimal discretization scheme in different velocity domains through the coordinated work of the three components mentioned above. At low speeds, the system defaults to time-domain discretization, benefiting from the computational regularity and direct description of time-varying processes provided by the fixed time step. As the speed gradually increases and the single-step spatial span approaches or exceeds a threshold, a verification feedback mechanism triggers a switch, and the system switches to spatial domain discretization, ensuring that the spatial resolution does not decrease with increasing speed. Throughout the simulation, multiple switches may occur, and the system always selects the most suitable discretization scheme for the current speed. This dynamic adaptive design effectively mitigates the speed-dependent discretization error generated when applying linear approximations to solve coupled multivariable nonlinear ordinary differential equation systems, ensuring the consistency and reliability of computational accuracy across the entire velocity domain.

[0118] From a numerical analysis perspective, the superiority of hybrid methods can be understood from the perspective of error order. In certain speed ranges, single-domain methods, due to inappropriate step size (time or space), may result in actual errors significantly exceeding the values ​​predicted by the theoretical error order. For example, in high-speed ranges, although the time step is fixed, the large spatial span of time-domain methods can lead to significant errors in position-dependent terms (such as…). , The variation within a step is approximated by a simple linear approximation, introducing additional sources of error. This error is not entirely controlled by the high-order accuracy of RK4, because RK4 assumes that the right-hand side of the differential equation can be well approximated by a polynomial within a step, but when the spatial span is too large, position-dependent nonlinear variations cannot be captured. The hybrid method, by limiting the maximum spatial span and the maximum time span, ensures that at any speed, the step size is not large enough to invalidate the linear approximation, thus maintaining the high-order accuracy advantage of the RK4 method.

[0119] Furthermore, the switching mechanism of the hybrid method is simple and straightforward, eliminating the need for complex adaptive step-size control algorithms (such as error estimation and step-size adjustment), thus reducing implementation complexity and computational overhead. Simultaneously, since only one discretization scheme is used each time, the complexity of parallel computation of multiple methods and result fusion is avoided. This simplicity allows the hybrid method to maintain high computational efficiency while ensuring accuracy, making it highly suitable for repeated calls within iterative optimization frameworks.

[0120] In summary, the spatiotemporal hybrid adaptive discretization method is a key technological innovation proposed in this invention for the simulation of maglev train speed curves. It deeply understands the essential characteristics of spatiotemporal coupling in maglev systems and the inherent limitations of single-domain discretization methods. Through a clever switching mechanism and high-precision numerical integration methods, it achieves high-precision simulation across the entire speed domain, providing a reliable numerical foundation for speed curve optimization and energy consumption calculation.

[0121] Constraint handling in simulation

[0122] Constraint handling is a crucial step in ensuring the physical feasibility, operational safety, and compliance with actual operational requirements of the simulated velocity curves. This invention employs an embedded constraint handling strategy, directly integrating constraint checking and violation handling logic into each state transition step of the simulation algorithm, rather than treating constraints as external penalties at the optimization level. The advantage of this design is that the simulation process itself can dynamically adjust control decisions to satisfy constraints, avoiding the generation of a large number of infeasible solutions. It also avoids problems such as difficulty in adjusting penalty coefficients and poor convergence in penalty function methods. Embedded constraint handling ensures that every velocity curve generated by simulation is feasible, which not only improves optimization efficiency but also enhances the reliability and practicality of the results.

[0123] Constraint verification and handling follow a hierarchical and progressive principle, checking and handling constraints step by step from hard constraints to soft constraints according to their importance and processing priority. Hard constraints are those that must be strictly satisfied; violating hard constraints will lead to system failure, safety accidents, or physical impossibility, and therefore must be prioritized. Soft constraints are those that can be relaxed to some extent but are desired to be satisfied, mainly involving non-critical indicators such as comfort.

[0124] Electrical parameter constraints are the most fundamental hard constraints and must be checked immediately after each state update. The traction power supply equipment of the maglev system has rated capacity limitations, including the maximum output current of the converter, the rated voltage of the transformer, and the maximum power of the entire traction system. Exceeding these limits may lead to equipment overload, protection device activation, or even equipment damage. A new state is calculated at each simulation step. and traction coefficient Then, the system immediately calculates the q-axis current based on these state variables. q-axis voltage and active power The calculation process involves the motor model described above, taking into account position-dependent resistance and inductance parameters.

[0125] The conditions for checking electrical parameters are as follows:

[0126] If any condition is not met, it indicates that the current traction coefficient... The requested force is too large, causing electrical parameters to exceed limits. In this case, the system employs a traction force limiting strategy for dynamic adjustment. Specifically, the traction coefficient is adjusted towards zero: for traction states ( ), reduce For braking state ( ), increase (That is, reducing the absolute value of the braking force). Each adjustment step is set to 0.01, a small value that allows for fine-tuning. After adjustment, the state transition and electrical parameters are recalculated, and the constraints are checked again. This process is iterated until all electrical parameters satisfy the constraints, or... Adjust to zero.

[0127] If adjusted to If the electrical constraints are still not met, the problem lies in the system's basic configuration. It's possible that the virtual speed limit configuration forces the train to operate at excessively high speeds at certain locations, while the motor characteristics at those locations cannot provide sufficient power to support that speed. In this case, the virtual speed limit configuration is physically infeasible, the simulation should terminate, and the candidate solution should be marked as infeasible. During the fitness evaluation phase, infeasible solutions are assigned extremely large objective function values ​​(such as positive infinity) and are automatically eliminated in subsequent solution selection processes.

[0128] Maximum speed limit constraints The algorithm automatically satisfies the state transition logic, requiring no additional checks or adjustments. When the train speed approaches the virtual speed limit of the current zone, the mapping function... It will automatically switch the operating mode to cruise ( At this point, the traction coefficient is adjusted to the equilibrium point. This ensures that the traction force exactly equals the resistance, allowing the train to maintain a constant speed. Since the speed is constant during cruise, it naturally won't exceed the virtual speed limit. This design transforms hard constraints into a natural consequence of the control logic, simplifying the complexity of constraint handling. It's important to note that the determination to enter cruise mode has a certain lead time, i.e., when the predicted speed... Switching to a speed limit when it is exceeded, rather than waiting until the speed is actually exceeded, avoids speed oscillation and overshoot.

[0129] Passenger comfort constraints primarily involve limiting the acceleration jerk. The acceleration jerk is defined as the derivative of acceleration with respect to time. This represents the rate of change of acceleration. An excessively high impact rate can cause passengers to experience sudden pushing or pulling, affecting comfort and even causing physical discomfort. This invention limits the impact rate by controlling the rate of change of the traction coefficient. According to the dynamic equation, acceleration... ,and ,therefore The acceleration impact rate is:

[0130] Within a short period of time, The change is relatively slow (mainly changing slowly with velocity and position), and the dominant term is... Therefore, limiting the impact rate is equivalent to limiting... The rate of change. In time-domain discretization, the change in the single-step traction coefficient should satisfy:

[0131] In spatial domain discretization, considering The single-step change should satisfy:

[0132] The system calculates the incremental update of the traction coefficient. At that time, it automatically limits the change to within the above threshold, ensuring that the change at each step does not exceed the allowable value. By gradually accumulating small changes, the traction coefficient can smoothly transition from the initial value to the target value while meeting the impact rate constraint. Whether increasing traction, decreasing traction, applying braking, or releasing braking, the whole process is gradual and comfortable.

[0133] Furthermore, at points where the speed limit changes, this invention implements a pre-deceleration mechanism to further ensure comfort. When a virtual speed limit ahead is detected to be about to decrease (…), the mechanism works as follows: When the train reaches the boundary of a new section, the system will not wait until it enters the boundary to initiate braking; instead, it will reduce the traction coefficient in advance to achieve smooth deceleration. The goal of pre-deceleration is to reduce the train's speed at the boundary of the section. It is already below the new speed limit. To avoid excessive impact caused by emergency braking. Pre-deceleration speed. The calculations take into account the decrease in train speed as the current traction coefficient gradually reduces to zero, ensuring sufficient lead time to handle speed limit changes. This mechanism embodies the concept of proactive control, adjusting control strategies in advance by anticipating future constraint requirements, thus achieving a smoother speed curve.

[0134] Dual-speed protection constraints are a unique safety mechanism of maglev systems, encompassing both emergency braking safety distance and loss-of-power coasting distance. During operation, maglev trains must ensure that, at any moment, in the event of an emergency requiring braking, they can safely stop before reaching the next auxiliary stopping area; simultaneously, if the train loses power (e.g., due to a power outage), it can still reach the auxiliary stopping area by coasting due to inertia, maintaining a speed above the minimum levitation speed to avoid losing levitation due to excessively low speed. These two constraints constitute dual-speed protection, ensuring safe operation of the train under both normal and abnormal conditions.

[0135] The system achieves dual-speed protection through forward-looking distance calculation and a dynamic braking triggering mechanism. In each simulation step, the system calculates two key distances: the safe braking distance and the safe braking distance. and gliding distance The safe braking distance indicates the distance from the current state. The distance required to decelerate to zero with maximum braking force. The calculation method is to establish the inverse dynamic equation of the braking process:

[0136] From the current speed Integrating to zero speed yields the braking distance. Due to the involvement of nonlinear drag terms, this integration is typically performed numerically. (Cashing distance) This indicates that after the train loses power, it will rely solely on inertia and resistance to glide from its current speed to its minimum levitation speed. (e.g., 4.17 m / s, corresponding to 15 km / h) the position that can be reached. The calculation method is similar, establishing the dynamic equation for unpowered gliding:

[0137] From the current speed Points to The gliding distance is obtained.

[0138] The system continuously monitors the current location. Distance to the next auxiliary parking area The location of the auxiliary stopping area is predefined in the track data and is typically located at the boundary of the power supply zone, in front of the station, or other safe areas. When the safe braking distance is detected to be approaching or exceeding the distance to the auxiliary stopping area, i.e. (in (This is a safety factor), and the system immediately triggers the forced braking mode. Specifically, the operating mode is forcibly set to braking. Even if the train is currently in traction or cruising mode, the braking is interrupted. The traction coefficient is adjusted to a negative value and gradually increases towards -1, applying maximum braking force to ensure the train can stop safely before the auxiliary stopping area. This forced braking mechanism simulates the safety protection logic of a real maglev system and has the highest priority; any other control objective must give way to safety.

[0139] At the same time, the system checks the gliding distance constraints: If this condition is not met, it means that even if the train currently loses power, it cannot reach the next auxiliary stopping area by inertia. Before reaching it, its speed will drop below the minimum levitation speed, posing a risk of losing levitation. This situation indicates that the virtual speed limit configuration is unreasonable, possibly limiting the speed too low at a certain location, causing the train to be unable to accumulate enough kinetic energy to cope with a possible power failure. The system marks this candidate solution as infeasible, terminates the simulation, and imposes a severe penalty in the fitness evaluation.

[0140] Speed ​​limit inflection point constraints are designed to prevent speeding at the inflection point where the speed limit decreases. This occurs at a certain location on the track. Virtual speed limit from Reduce to At that time, if the train is The vehicle travels at high speed until the inflection point, and only then begins to brake, potentially not having enough time to reduce speed before entering the next section. This could lead to speeding. To avoid this, the system calculates the braking distance required to brake from the current state to the next zone's speed limit. and the safe distance to the inflection point Comparison:

[0141] If this condition is not met, it indicates that the current speed is too high or too close to the inflection point. Braking must be initiated in advance or the coasting intensity increased to prevent overspeeding and entering the low-speed restriction zone. The system's response strategy is to switch the operating mode to braking, or, if already coasting, to continue coasting while monitoring speed reduction. This proactive inflection point constraint check ensures that the speed curve meets the virtual speed limit requirements throughout the entire line.

[0142] After summarizing all constraint check results, a state feasibility determination is formed. If any hard constraint (electrical parameters, dual-speed protection) is violated and cannot be recovered through dynamic adjustment, the virtual speed limit configuration is determined to be infeasible, and the simulation terminates prematurely. Upon termination, the system returns a special flag indicating that the candidate solution is infeasible, and records the type of constraint violation and the location of the violation for subsequent analysis and debugging. During the iterative optimization process, infeasible solutions are assigned an objective function value during the fitness evaluation phase. In the solution selection step, the solution is automatically eliminated and will not be passed on to the next generation. Through this natural elimination mechanism, the optimization algorithm gradually converges to the feasible solution space, and the optimal solution found in the end must satisfy all constraints.

[0143] By employing this embedded constraint handling mechanism, this invention effectively avoids the numerical instability and convergence difficulties that can result from constraints being used as external penalty terms in traditional optimization methods. A common problem with penalty function methods is the selection of the penalty coefficient: if the coefficient is too small, the constraint is not effectively enforced; if the coefficient is too large, the objective function becomes steep, gradient information is distorted, and the search efficiency of the optimization algorithm is affected. The embedded method integrates constraint checking into the simulation process, naturally satisfying constraints using the simulation's physical model and control logic, avoiding artificially introduced penalty terms. Furthermore, since each velocity curve generated by the simulation is physically feasible and operationally safe, the optimization algorithm's search process is entirely within the feasible region, improving search efficiency and result quality. This design concept fully reflects the invention's profound understanding of the operating mechanism of maglev systems and its high regard for practical engineering applications.

[0144] Simulation algorithm flow for speed curve of hybrid maglev train in spatiotemporal domain

[0145] The preceding sections introduced the key technical elements of the simulation algorithm, including state definition, state transition, hybrid discretization, and constraint handling. These elements are organically integrated through a complete algorithm flow, forming a spatiotemporal hybrid maglev train speed curve simulation algorithm. The algorithm's inputs are virtual speed limit configurations and fixed track and vehicle parameters, while its outputs are detailed speed curves and performance indicators such as running time and energy consumption. The overall algorithm flow follows the logic of initialization → cyclic simulation → constraint checking → state update → termination determination, with the specific steps as follows: First, the algorithm performs initialization. It sets the initial state. The position, speed, time, energy consumption, and current are all zero, and the operating mode is as follows: The traction coefficient is zero. Initialize an empty velocity curve data structure. It is used to store the sequence of state points during the simulation process. It reads line data, including the endpoint location. Fixed parameters include maximum speed limits at each location, gradient, stator segment parameters, power supply mode, and auxiliary parking area location. The input virtual speed limit vector is read. Determine the speed limit for each partition.

[0146] Then, the algorithm enters the main loop, with the loop condition being that the current position has not reached the endpoint: In each loop, first determine the current position. Determine the virtual speed limit zone you are in. and related speed limit parameters The location of the next auxiliary parking area And if a speed limit inflection point exists, .

[0147] Next, use the mapping function. Calculate the running mode status The mapping function determines whether to use traction, cruise, coasting, or braking mode based on the relationship between the current speed and the virtual speed limits ahead and behind, as well as the predicted future speed. The specific decision-making logic follows the rules described in Section 4.1.2 above.

[0148] Update traction and braking coefficients based on operating mode status. The update process uses formulas. ,in Direction control vector constrained by impact rate The direction of increase or decrease is determined based on the operating mode and the current coefficient value.

[0149] If the current operating mode is not braking ( ), and is in traction or cruise mode ( or If so, a proactive safety check should be performed. The safe braking distance should be calculated. Braking distance at the inflection point If found and (For all inflection points) If the current condition indicates that traction or cruising can continue without violating safety constraints, then the state transition function should be applied. Calculate the next state. Otherwise, the safety margin is insufficient, and the system must switch to braking mode. .

[0150] If you are in a coasting or preparing to decelerate ( and or In addition to checking the safe braking distance and the inflection point braking distance, it is also necessary to check the pre-deceleration speed. Is it below the current speed limit? If all conditions are met, continue in the current mode; otherwise, switch to braking.

[0151] If you are already in braking mode ( If the traction coefficient is updated (it is now negative, increasing the braking force), the state transition function is applied using the braking parameters. Calculate the next state and update the running mode state vector based on the new state.

[0152] State transition function The execution involves hybrid spatiotemporal adaptive discretization computation. Based on the current velocity and the discretization method of the previous step, the system determines whether to use time-domain or spatial-domain discretization in this step. If time-domain discretization is used, the RK4 method with a fixed time step is employed. The state update is calculated, and then a verification feedback mechanism is used to check whether the spatial span is within the allowable range. If the spatial span is too large, the system switches to the spatial domain and re-applies the RK4 method with a fixed spatial step size. Calculation. The next state is finally obtained. .

[0153] During state transitions, electrical parameter constraints must be checked at each step. The q-axis current, voltage, and power are calculated; if they exceed limits, the traction coefficient is adjusted and recalculated until the constraints are met or the traction coefficient is zero. If the constraints are still not met even after zeroing, the simulation is marked as infeasible and terminated.

[0154] After the status update is complete, calculate the glide distance based on the current status. .if This indicates that the taxiing distance constraint of dual-speed protection is satisfied, and the current state is... Stored in velocity curve data structure In the simulation, the point is used as a reference on the speed curve. The simulation then continues in a loop to the next step. If the coasting distance constraint is not met, it indicates that the virtual speed limit configuration is infeasible, the simulation terminates prematurely, and an infeasibility flag is returned.

[0155] When the position reaches or exceeds the finish line At this point, the main loop ends. The algorithm starts from the velocity curve data structure. Time to extract the final state and energy consumption This returns the runtime and energy consumption metrics under the virtual speed limit configuration. It also outputs a complete speed curve, including the location, speed, and time of each state point, which can be used for subsequent detailed analysis and visualization.

[0156] The pseudocode representation of the above algorithm flow can be found in Algorithm 1, which details the condition judgments and operation order of each step.

[0157] Algorithm 1: Simulation Algorithm Flow for Spatiotemporal Hybrid Maglev Train Speed ​​Curve

[0158] (2) Virtual speed limit generation mechanism

[0159] The virtual speed limit generation mechanism is the second core component of this invention. Its main function is to generate and manage the decision variables—virtual speed limit configurations—in the optimization process. In traditional train speed curve optimization methods, decision variables are usually the train's state variables, such as speed, acceleration, traction force, or current at various times or locations. These variables are typically continuous high-dimensional vectors with extremely large decision spaces, and complex constraints exist between them (dynamic constraints, electrical constraints, safety constraints, etc.), making the optimization problem difficult to solve. This invention creatively introduces the concept of virtual speed limits, transferring the decision variables from a continuous state space to a discrete speed limit space, thereby significantly reducing the problem's dimensionality and the optimization difficulty.

[0160] The design of the virtual speed limit generation mechanism is based on optimal driving strategy theory and the operational characteristics of maglev systems. Optimal driving strategy posits that energy-optimal train operation typically follows a "maximum power-cruising-coasting-maximum braking" pattern, with speed limits being a key factor triggering these pattern transitions. By adjusting the size and distribution of speed limits, the train's operation can be indirectly controlled, thereby influencing energy consumption. The virtual speed limit generation mechanism concretizes this idea, designing a systematic method to generate reasonable speed limit configurations that ensure both physical constraints and operational requirements are met, while also possessing sufficient diversity to support optimization searches.

[0161] Virtual speed limit concept

[0162] Virtual speed limits are artificially set speed restrictions used to guide train operation, but they differ from the physical speed limits of the track itself (determined by factors such as curve radius and gradient). The introduction of virtual speed limits aims to transform the optimization problem from complex state control into relatively simple parameter adjustment. In this invention, virtual speed limits serve as input parameters to the simulation algorithm, replacing the state variables that need to be directly optimized in traditional methods, thus forming a new decision variable framework.

[0163] Specifically, maglev lines are divided into There are 1 virtual rate-limiting partitions, each with a length of 1. The virtual rate-limiting partitions are divided uniformly, meaning each partition is of equal length. This uniform division simplifies management and calculation. Number of partitions. Based on the total length of the line and partition length Decide: ,in Indicates rounding up. Virtual speed limit vector. Defined as an ordered tuple, where each element Representing the The speed limit value imposed on trains within each virtual speed limit zone:

[0164] This vector represents the decision variables in the optimization problem. The optimization algorithm adjusts the values ​​of each element of the virtual speed limit vector to find the configuration that minimizes energy consumption while satisfying runtime constraints. The virtual speed limit vector has the following dimensions: Compared to traditional methods, which require optimizing a number of state variables (potentially thousands of discrete time or spatial points for velocity, acceleration, etc.), the dimensionality is significantly reduced, and the size of the optimization problem is significantly shrunk.

[0165] Each virtual speed limit must meet certain constraints to ensure its physical rationality and operational feasibility. Upper bound Set to not exceed the maximum speed limit of this zone. The maximum speed limit for a railway line is determined by the line's physical conditions, such as curve radius, gradient, and track quality. It is a hard constraint; no virtual speed limit can be exceeded, otherwise train operation would be unsafe. Lower Bound This setting is to prevent the average speed from being too low, thus failing to meet the predetermined running time requirements. Each virtual speed limit satisfies:

[0166] These upper and lower bound constraints ensure that the virtual speed limit is within a reasonable range, neither violating safety restrictions due to being too high nor causing low operating efficiency due to being too low.

[0167] The ingenuity of the virtual speed limit concept lies in its transformation of a complex control problem into a parameter selection problem. Given a virtual speed limit vector, the spatiotemporal hybrid maglev train speed curve simulation algorithm automatically generates the corresponding speed curve through state transition logic and optimal driving strategy principles, without requiring manual intervention or complex trajectory planning. The virtual speed limit is equivalent to setting a series of "speed upper limits" for the train. During operation, the train will try to approach these upper limits (through traction acceleration and cruising), and adapt to changes in the speed limit through coasting or braking when necessary. By adjusting the magnitude and distribution pattern of the virtual speed limit, the timing and extent of the train's acceleration, cruising, coasting, and braking can be indirectly controlled, thereby affecting energy consumption.

[0168] Compared to directly optimizing speed or traction, virtual speed limits offer several advantages as decision variables. First, the dimensionality is significantly reduced, from thousands to tens of dimensions, drastically shrinking the search space. Second, virtual speed limits are physically meaningful, easy to understand and adjust, and have good interpretability, making them easier for operators to understand and accept. Third, virtual speed limits align with the actual operation and management methods of maglev systems, which also manage train operation by setting speed limits; therefore, optimization results can be directly translated into operational strategies. Finally, adjustments to virtual speed limits do not directly violate dynamic or electrical constraints, which are automatically satisfied during the simulation generation phase, avoiding the generation of numerous infeasible solutions during optimization.

[0169] The introduction of the concept of virtual speed limit is a significant innovation of this invention, which changes the traditional approach to optimization methods and opens up a new technical route. By elevating the decision-making layer from the state space to the parameter space, this invention achieves dimensionality reduction and simplification of the optimization problem, laying the foundation for efficiently solving the speed curve optimization problem of maglev trains.

[0170] Virtual speed limit generation strategy

[0171] The core task of the virtual speed limit generation mechanism is to systematically generate diverse virtual speed limit configurations that meet constraints based on route characteristics and optimization requirements. If the generation of virtual speed limits is completely random, while diversity can be guaranteed, most random configurations may be unreasonable. For example, excessively large differences in speed limits between adjacent zones, too few or too many cruise segments, or a disconnect from the route's maximum speed limit distribution. These unreasonable configurations can lead to high energy consumption, unevenness, or even infeasibility in the simulated speed curves. Therefore, an intelligent generation strategy needs to be designed to guide the generation process towards configurations that conform to the principles of optimal driving strategies while ensuring diversity.

[0172] The virtual speed limit generation strategy of this invention is based on a virtual speed limit block partitioning framework. The basic idea of ​​this framework is to aggregate virtual speed limit partitions into several virtual speed limit blocks. Each block contains a group of contiguous partitions with similar physical characteristics or operational requirements. The virtual speed limit values ​​within a block are organized according to specific rules, and the blocks remain relatively independent. This hierarchical design preserves the local optimal structure of the speed curve while reducing the complexity of optimization through block-level operations.

[0173] The specific method for dividing virtual speed limit blocks is as follows: First, based on the distribution of the maximum speed limit of the line, divide... The virtual speed limit partitions are aggregated into A virtual speed limit block The aggregation rule is that if adjacent partitions have the same maximum speed limit (i.e., ... If they are grouped into the same block, then they are grouped together.

[0174] The internal structure of each block embodies the core elements of the optimal driving strategy. Include One virtual speed limit zone ( The virtual speed limit values ​​within a block are organized according to a "cruising-decreasing" pattern. Specifically, the cruising interval length is first determined for each block. , indicating the previous block Each zone maintains the same virtual speed limit (cruise state). The cruise interval is determined using a randomized method to increase the diversity of candidate solutions.

[0175] in It is the cruise ratio coefficient. By randomizing the cruise ratio, the cruise length distribution of different candidate solutions within the block varies, enhancing the diversity of solutions.

[0176] The discretization of virtual speed limits uses uniform granularity. This parameter defines the minimum increment between virtual rate limits. The choice of granularity needs to balance optimization accuracy and computational efficiency: too large a granularity will result in too few selectable rate limits, limiting optimization accuracy; too small a granularity will cause the number of selectable values ​​to surge, increasing computational load. According to numerical experiments, A value of around 0.05 m / s (approximately 0.18 km / h) is suitable, providing sufficient accuracy without excessively increasing the search space. All virtual speed limit values ​​are... An integer multiple of a certain base value is added to form a discrete velocity grid.

[0177] The complete formula for generating virtual speed limit rules is as follows:

[0178] This formula covers four scenarios, corresponding to different speed limit change modes. The first scenario: The maximum speed limit of the current zone is higher than that of the next zone (…). And it is not the first partition. This indicates that we are about to enter a region with a reduced speed limit, and the virtual speed limit should be proactively reduced to adapt in advance. Specifically, the value is the virtual speed limit of the previous zone minus the granularity. However, it cannot be lower than the lower limit or higher than the upper limit, therefore it is used and Function constraints. This gradually decreasing design avoids sudden and sharp drops in the virtual speed limit at the speed limit change point, which helps to generate a smooth speed curve.

[0179] The second scenario: The maximum speed limit of the current partition is the same as that of the previous partition. And it is in the intra-block cruise segment ( At this point, the virtual speed limit remains unchanged and is equal to the virtual speed limit of the previous zone. This reflects the characteristic of maintaining a constant speed limit during the cruise phase, allowing the train to run at high speeds for extended periods and reducing energy consumption.

[0180] The third scenario: The current partition has the same maximum rate limit as the previous partition and is in a decreasing segment within the block ( At this point, the virtual speed limit decreases progressively with a fixed granularity. The decrease amount is... This means that each partition in the decreasing segment is one granularity lower than the previous partition. This linear decrease ensures a smooth transition of the speed limit, avoiding drastic changes.

[0181] The fourth scenario: The maximum speed limit of the current partition is lower than that of the next partition. This indicates that the train has entered a region with an increased speed limit, at which point the virtual speed limit needs to be redefined. Because the speed limit has increased, the train has the opportunity to accelerate to a higher speed; therefore, the virtual speed limit value is randomly generated within the new permissible range, denoted as . ,in This indicates a uniform distribution. Random generation increases the diversity of solutions and avoids all candidate solutions choosing the same strategy during the rate-limited ascent phase.

[0182] Based on the above generation rules, the virtual speed limit configuration, while satisfying the constraints, embodies the basic pattern of the optimal driving strategy: cruising first and then gradually decreasing speed within the same physical characteristic section, slowing down in advance at the speed limit reduction point, and appropriately randomizing at the speed limit increase point to increase exploratory power. This design makes the generated virtual speed limit configuration both reasonable and diverse, providing a good initial solution and mutation basis for iterative optimization.

[0183] Figure 3This paper demonstrates the specific implementation of the virtual speed limit block partitioning framework for the virtual speed limit generation mechanism. Within each block, the distribution pattern of virtual speed limits is represented by stepped solid lines. The figure illustrates the spatial distribution characteristics of virtual speed limits and the hierarchical structure of the virtual speed limit block partitioning. This structured generation method is key to the optimization capabilities of this invention, significantly reducing the generation of inconsistencies and guiding the optimization search in a favorable direction.

[0184] Representation of virtual speed limit vector

[0185] Complete virtual speed limit vector It can be represented as all Serialization of blocks:

[0186] in Indicates the first The first block The partition (the th partition in the global context) The virtual rate limit value (for each partition). This triple index representation clarifies the hierarchical relationship of the virtual rate limit value: global partition index... Local partition index within a block and block index .

[0187] The virtual speed limit generation mechanism provides initial and mutated solutions for the iterative optimization process through virtual speed limit block partitioning and generation strategies. The generated virtual speed limit configurations not only satisfy all hard constraints (upper and lower bounds, discretization) but also reflect the basic characteristics of the optimal driving strategy (cruising, smooth transition, moderate randomness), improving the efficiency and convergence speed of the optimization algorithm. This generation mechanism is one of the important innovations of this invention, and together with the hybrid spatiotemporal simulation algorithm and the iterative optimization process, it constitutes a complete optimization technology system.

[0188] (3) Iterative optimization process

[0189] The iterative optimization process is the third core component of this invention, acting as a strategic coordinator to drive the entire optimization process towards the optimal solution. The input to this process is the candidate solution set generated by the virtual rate-limiting mechanism and the fitness information obtained from the hybrid spatiotemporal simulation algorithm. The output is the optimal virtual rate-limiting configuration after iterative improvement. The iterative optimization process employs a metaheuristic algorithm framework, combining mechanisms such as population evolution, optimal solution preservation, and block-level operations to achieve an organic combination of global search and local optimization.

[0190] The optimization process is designed to fully consider the block-like structure characteristics of the virtual rate limit, and specifically incorporates two operators: block recombination and block update. These operators, while preserving locally optimal structures, generate new candidate solutions through recombination and updates, enhancing the algorithm's exploration capability. Simultaneously, the optimal solution preservation strategy ensures that the best solution in each generation does not degenerate, while the adaptive update probability mechanism dynamically adjusts the mutation intensity based on the block length, enabling the algorithm to automatically balance exploration and utilization during the optimization process.

[0191] Overview of Iterative Optimization Process

[0192] The iterative optimization process follows the classic evolutionary algorithm framework, including initialization, fitness evaluation, selection, updating, recombination, and termination determination. The entire process continuously improves the quality of candidate solutions through iterative loops until the termination condition is met. Unlike standard evolutionary algorithms, this invention designs specialized operators for the unique structure of virtual rate limits, making the algorithm more efficient and applicable.

[0193] The iterative optimization process consists of six main steps: Step 1 is initialization, generating an initial candidate solution set; Step 2 is fitness evaluation, calling simulation algorithms to calculate the objective function value of each candidate solution; Step 3 is solution selection, selecting the optimal solution based on fitness ranking; Step 4 is solution update, generating new candidate solutions through block recombination and block update; Step 5 is generation of the next generation of solutions, merging optimal solutions and new solutions to form the next generation population; Step 6 is iteration termination and optimal solution selection, determining whether the termination condition has been met and outputting the optimal solution. The following sections elaborate on the technical details of each step.

[0194] Step 1: Initialization

[0195] The initialization phase is the starting point of the iterative optimization process, and its quality directly affects the efficiency and effectiveness of subsequent optimizations. This invention employs a diversity-oriented initialization strategy, aiming to generate a widely distributed and high-quality initial candidate solution set. The size of the initial solution set is... indivual, It is a key parameter of the algorithm, and is usually determined based on the problem size and computational resources.

[0196] The specific initialization steps are as follows: For each candidate solution The virtual rate limit generation mechanism is invoked to generate a complete virtual rate limit configuration. The generation process strictly follows the virtual rate-limited block division and virtual rate-limited generation strategy.

[0197] Step 2: Fitness Assessment

[0198] Fitness evaluation is a core step in the optimization process. Its role is to quantify the merits of each candidate solution, providing a basis for subsequent selection and updates. In this invention, fitness evaluation is achieved by calling a spatiotemporal hybrid maglev train speed curve simulation algorithm, which transforms the virtual speed limit configuration into performance indicators such as running time and energy consumption, and then calculates the objective function value.

[0199] For the Each candidate solution of the generation ( The fitness evaluation process is as follows: First, the virtual speed limit configuration and fixed line vehicle parameters are input into the simulation algorithm, and Algorithm 1 is called to perform a complete simulation calculation. Based on the virtual speed limit and line conditions, the simulation algorithm simulates the train's journey from the starting point to the destination, generates detailed speed curves, and records information such as the position, speed, running time, and energy consumption of each state point.

[0200] After the simulation is completed, key performance indicators are extracted: runtime. (Total time taken by the train from the starting point to the destination, in seconds) and energy consumption (Total energy output by the traction power supply system, in kilowatt-hours). These two indicators reflect the performance of the speed curve in terms of time efficiency and energy efficiency, respectively.

[0201] objective function Taking into account both operating time deviation and energy consumption, it is defined as a weighted combination of the two:

[0202] in, These are predefined runtime requirements. It is the weighting coefficient for runtime deviation, reflecting the importance of on-time performance. This is a weighting coefficient for energy consumption, reflecting the importance of energy efficiency. It can be adjusted... and The relative size can balance the goals of timeliness and energy efficiency.

[0203] For candidate solutions deemed infeasible in the simulation (such as violating dual-velocity protection constraints, exceeding electrical parameter limits and being unadjustable), the fitness evaluation returns a maximal objective function value. (In actual calculations, a very large number is used, such as...) (This is indicated by the text). This process ensures that infeasible solutions are inevitably eliminated in subsequent selections, and the optimization process always takes place within the feasible region.

[0204] Complete all After evaluating the fitness of each candidate solution, a sequence of objective function values ​​is obtained. These values ​​will be used for sorting and selection in the next step.

[0205] Step 3: Solve the selection

[0206] The purpose of the solution selection step is to select the best performing individuals from the candidate solutions of the current generation, retain them directly as the best solutions for the next generation, and use them as the basis for generating new solutions.

[0207] The specific selection process is as follows: First, based on the objective function value, select the... generation The candidate solutions are sorted in ascending order. A smaller objective function value indicates a higher quality solution (lower energy consumption and runtime close to the objective). The sorted solution yields an ordered sequence. Let the sorted solution be the nth solution. The solution is ,in It is a sorting and permutation function that satisfies .

[0208] Then, select the first sorted items. Each solution is a set of optimal solutions. ,in It is the optimal solution retention ratio parameter.

[0209] optimal solution set Defined as:

[0210] These optimal solutions will directly proceed to the next step. In each iteration, no modification or verification is required, ensuring that high-quality solutions already found are not lost during the iteration process. The optimal solution preservation strategy is a key mechanism to guarantee the convergence of the algorithm, which ensures that the optimal objective function values ​​of each iteration form a non-increasing sequence: This theoretically ensures that the optimization process will not degenerate.

[0211] In addition to the optimal solution, it is also necessary to generate New candidate solutions are generated to populate the next generation of the population, keeping the population size constant. These new solutions are generated through the solution update process in step 4, providing opportunities for the optimization search to explore new regions and preventing the algorithm from converging prematurely.

[0212] Step 4: Uninstall Update

[0213] The solution update step is the core step in generating new candidate solutions. By modifying and reorganizing existing solutions, new solutions with different characteristics are generated. This invention designs two specialized sub-processes: block reorganization and block update. These two sub-processes make full use of the block structure characteristics of virtual rate limiting, introducing beneficial mutations while preserving excellent patterns.

[0214] Block reorganization process

[0215] The purpose of the block recombination process is to generate a new solution structure by exchanging and recombining virtual rate-limiting blocks. This process is inspired by the crossover operation in genetic algorithms, but simplified to fit the block structure. For each candidate solution to be updated... (Usually selected from outside the optimal solution set or randomly chosen from the optimal solution set as the parent), the system first extracts all of its... A virtual speed limit block .

[0216] Then, a random reorganization decision is performed on each block. A uniformly distributed random number is generated. Compared with the threshold of 0.5: If Then retain the current block. Otherwise, replace the block at that position with the block at the next position. For the last block ( The "next position" loop returns to the first block. This achieves circular replacement. The mathematical expression for block reorganization is:

[0217] The new solution obtained after recombination Composed of the recombined block sequence:

[0218] Block update process

[0219] The block update process selectively regenerates the internal structure of certain blocks based on the recombined solution, enabling local search and fine-tuning. The core of this process is calculating the update probability of each block, the magnitude of which is related to the block length.

[0220] For each reorganized block Its update probability The calculation is as follows:

[0221] in It is the number of partitions within that block. These are global control parameters. The design of this formula is based on a binomial probability model: assuming each partition has independent... If the probability needs to be updated, then the probability that at least one partition of the entire block needs to be updated is... . The larger the value, the more sensitive the update probability is to the block length; The smaller the value, the lower the baseline level of the update probability.

[0222] Regenerated blocks Replace with the newly generated virtual speed limit sequence:

[0223] Blocks not selected for updating remain in their reorganized state. The block update process provides the algorithm with a mechanism to escape local optima. When optimization stagnates and the objective function value changes very little over multiple generations, block updates can introduce significant changes, producing solutions that are significantly different from the current population, which helps explore other regions of the solution space. Simultaneously, because updates are probabilistic and adjusted by block length, not all blocks are updated, thus preserving some of the desirable characteristics of the original solution and achieving a balance between aggressive exploration and conservative inheritance.

[0224] The combination of block recombination and block update enables the solution update process to possess multi-level search capabilities. Block recombination explores at the macro level (combinations between blocks), while block update adjusts at the micro level (internal structure of blocks). Through these two processes, the algorithm can search the solution space at different granularities, avoiding the blindness of completely random mutation and overcoming the limitations of simple local search. This multi-level, structured mutation strategy is a key innovation of the iterative optimization process in this invention.

[0225] Step 5: Generation of the next generation of solutions

[0226] After the update step, the following was generated: A new candidate solution, denoted as The next generation of complete candidate solution sets is formed by merging the optimal solution set and the new solution set:

[0227] This merging strategy ensures that the next generation population size remains at [a certain level]. ,in This is a superior solution selected from the previous generation of optimal solutions. The new solutions are generated through mutation. The composition of the population reflects a combination of elitism and diversity maintenance: optimal solutions guarantee the stability and convergence of the optimization process, while new solutions provide the possibility of exploring new regions.

[0228] After the generation of the new generation solution is completed, the algorithm returns to step 2. The fitness of all candidate solutions is evaluated, and a new round of iterations begins. This cycle repeats continuously, with each generation improving upon the previous one, gradually approaching the optimal solution.

[0229] Step 6: Iteration Termination and Optimal Solution Selection

[0230] Iterative optimization processes require a clear termination condition to determine when to stop iterating and output the final result. This invention uses the maximum number of iterations as the primary termination condition, i.e., when the number of iterations reaches a certain threshold... Reaching the preset maximum value The algorithm terminates when the maximum number of iterations is reached. It is a parameter that needs to be preset based on the complexity of the problem and the computing resources.

[0231] Choosing the maximum number of iterations requires balancing optimization quality and computation time. If... If the value is too small, the algorithm may terminate before fully searching the solution space, resulting in a low-quality solution. If... If the value is too large, although it may further improve the quality of the solution, the marginal benefit diminishes and the computation time increases significantly.

[0232] When the iteration termination condition is met, the algorithm enters the optimal solution selection phase. From all... Generations (including the initial generation 0 to the final generation) From the candidate solutions generated by (e.g., the one with the smallest objective function value) is selected as the optimal solution:

[0233] Due to the optimal solution preservation strategy, the optimal solution usually appears in later generations, and the optimal solution in the final generation is the historical optimal solution. However, to be on the safe side, the algorithm checks the records of all generations to ensure that no possible optimal solution is missed.

[0234] Select the optimal virtual speed limit configuration Then, the algorithm calls the hybrid spatiotemporal simulation algorithm again to perform a final detailed simulation of the configuration, generating a complete optimal velocity curve. This velocity curve contains information on all state points from the starting point to the ending point, including the position, velocity, time, energy consumption, current, and operating mode of each point, which can be used for subsequent detailed analysis, visualization, and actual operation implementation.

[0235] The output of the optimal solution also includes a summary of key performance indicators: optimal running time. Optimal energy consumption Optimal objective function value The data also includes comparative data with baseline solutions, such as the percentage reduction in energy consumption and deviations in operating time. This information provides a quantitative basis for evaluating the effectiveness of optimization and for making implementation decisions.

[0236] Algorithm convergence and adaptive mechanism analysis

[0237] The iterative optimization process of this invention ensures the convergence and optimization effect of the algorithm through a carefully designed mechanism. The optimal solution preservation strategy is the theoretical guarantee of convergence; it ensures that the optimal solution in each generation is monotonically non-increasing, mathematically guaranteeing that the algorithm will not degenerate. Let the... The optimal objective function value is Then we have:

[0238] This monotonic property is directly caused by the preservation of optimal solutions: since the optimal solution of each generation is directly passed to the next generation, the candidate solution set of the next generation contains at least the optimal solution of the previous generation, so the optimal value of the next generation cannot be worse than that of the previous generation. This monotonic convergence property is very important in practical applications, as it ensures that the quality of the solution steadily improves with iteration, without significant fluctuations or degradation.

[0239] Adaptive update probability mechanism This gives the algorithm the ability to automatically adjust the search intensity. In the early stages of optimization, the population diversity is high, the block lengths of different candidate solutions are widely distributed, and the variance of the update probability is large. Some solutions' long blocks will be frequently updated, introducing significant changes and maintaining strong exploration capabilities. As optimization progresses, inferior solutions are eliminated, and the remaining solutions tend to be similar. The block structure gradually stabilizes, the differences in update probabilities narrow, and the algorithm naturally shifts to a more refined local search. This adaptability requires no manual parameter tuning; it is entirely achieved automatically by the algorithm based on the current population state, demonstrating the intelligence of the design.

[0240] The core advantage of this technical solution lies in: reducing the dimensionality of high-dimensional optimization problems through virtual speed limiting, ensuring the computational accuracy of the entire velocity domain through a spatiotemporal hybrid discretization method, minimizing energy consumption through iterative optimization, and finally obtaining the optimal velocity curve under multiple constraints.

[0241] In summary, this invention provides a simulation optimization method for the operating speed curve of maglev trains based on virtual speed limits. It proposes a spatiotemporal hybrid adaptive discretization method that dynamically switches between time and spatial domain computation modes according to train speed, ensuring time resolution at low speeds and maintaining spatial resolution at high speeds. This fundamentally eliminates the speed-dependent errors caused by single-domain methods and achieves consistent numerical accuracy across the entire speed domain. Furthermore, this invention introduces virtual speed limits as a core decision variable, transforming the complex high-dimensional continuous control problem into a structured discrete input sequence problem. By adjusting the distribution of virtual speed limits, indirect control of traction, cruise, coasting, and braking processes is achieved, significantly reducing the optimization dimensionality. Combined with a virtual speed limit block partitioning mechanism and embedded constraint processing strategy, this method can automatically generate physically feasible optimal speed curves under multiple constraints, including dual-speed protection, safe braking distance, and passenger comfort. Compared with existing technologies, this invention significantly reduces operating energy consumption and greatly improves computational efficiency while ensuring safety and comfort, providing a more accurate, efficient, and engineering-feasible solution for maglev train speed curve optimization.

[0242] The key to this invention lies in introducing a virtual speed limit as the core decision variable for maglev speed curve simulation optimization. This method divides the maglev line into several virtual speed limit zones, each with a virtual speed limit value. The upper bound of the virtual speed limit is constrained by the physical speed limit of the line, while the lower bound is set according to operating time requirements. By systematically adjusting the virtual speed limit configuration, the acceleration, cruising, coasting, and braking modes of the train are indirectly controlled, minimizing the energy consumption of the traction power supply system while meeting predetermined operating time requirements.

[0243] On the other hand, this invention provides a hybrid discretization algorithm to solve the speed-dependent error in the numerical solution of the dynamic equations of maglev trains. Its key technical feature lies in dynamically selecting the time-domain or spatial-domain discretization scheme based on the train speed. This algorithm sets a fixed time step. and spatial step size In each simulation step, time-domain discretization is first attempted to calculate the spatial span. ,like If the result is in the time domain, it is accepted; otherwise, it switches to spatial domain discretization. In the low-speed range, time domain discretization ensures sufficient time resolution to accurately characterize transient dynamic characteristics, while in the high-speed range, spatial domain discretization ensures sufficient spatial resolution to accurately capture position-dependent changes in motor parameters.

[0244] Third, this invention provides a mechanism for systematically generating virtual speed limit configurations. Its key technical feature lies in organizing virtual speed limits using a virtual speed limit block partitioning framework. This mechanism aggregates virtual speed limit partitions into several virtual speed limit blocks based on the distribution of the line's maximum speed limit. Sections within the same block have the same maximum speed limit. Determine the cruise interval length for each block. Within the cruise interval, the virtual speed limit remains constant, reflecting the cruise characteristics of the optimal driving strategy. In zones after the cruise interval, the virtual speed limit is set at a fixed granularity. It gradually decreases, forming a step-like descent pattern.

[0245] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0246] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0247] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0248] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A simulation optimization method for the operating speed curve of a maglev train based on virtual speed limits, characterized in that, include: S1 describes the operation process and electrical characteristics of the maglev train by constructing a discrete state-space model; S2 describes the operation process and electrical characteristics of the maglev train based on the discrete state-space model, and calculates all states of the maglev train operation process through the transformation function. S3 calculates the initial speed curve based on all states during the operation of the maglev train using a mapping function. S4 Based on all states of the maglev train operation process and the initial speed curve, the maglev train operation simulation is carried out through the spatiotemporal domain hybrid adaptive speed curve simulation method, and the speed of the maglev train is adjusted through the virtual speed limit generation mechanism, so that the optimal speed curve of the maglev train operation process can be obtained after the maglev train operation simulation process. The optimal speed curve during the operation of a maglev train is used for the control optimization of the maglev train.

2. The simulation and optimization method for the operating speed curve of a maglev train according to claim 1, characterized in that, Step S1 includes: Through Construct a discrete state-space model; where: Position status (meters); Speed ​​status (m / s); Time status (seconds); The cumulative energy consumption state (kilowatt-hours) represents the total energy consumption from the starting point to the current state point; This represents the q-axis current state (Amperes), used for voltage calculation and tracking current changes; To ensure a uniform traction and braking coefficient, the range is from -1 to 1, with positive values ​​representing traction force, negative values ​​representing braking force, and zero representing no force that can be applied. Let be the operating mode state vector, representing the vehicle's operating state at the end of the i-th simulation step; in the operating mode state vector, the traction variable Capture traction dynamics, where -1 represents the traction coefficient. The value decreases from the current value to 0, where 0 indicates no traction and 1 indicates that the traction coefficient increases from the current value to 1; cruise variable. It's binary; 0 indicates non-cruise mode, and 1 indicates constant speed cruise mode. Lazy variable. Distinguish between non-coasting state 0 and coasting state 1. In coasting state, the vehicle moves under inertia without power input; braking variable. Capture braking dynamics, where -1 represents the braking coefficient. The value decreases from the current value to 0, where 0 indicates no braking and 1 indicates that the braking coefficient increases towards -1.

3. The simulation and optimization method for the speed curve of a maglev train according to claim 2, characterized in that, Step S2 includes: By transforming the functional expression The train state transition values ​​are calculated, and the operation process of the maglev train is described by these values; where: Indicates the first i The interval is the first r and the r Maximum speed limit at position +1 The constraint set includes electrical parameter constraints, maximum speed limit constraints, acceleration impact rate limits, boundary state constraints, and dual-speed protection constraints; the constraint set is expressed as follows: Calculated; where: These represent electrical parameter constraints, including upper limits for q-axis current, q-axis voltage, and active power, which are derived from the rated capacity of traction substations and transmission facilities. This represents the maximum speed limit constraint, ensuring that the train speed does not exceed the virtual speed limit of the current zone; This represents the acceleration impact rate limit, used to ensure passenger comfort by limiting the rate of change of acceleration to no more than a preset threshold. Represents boundary state constraints, specifying the velocity, position, and time conditions for the start and end points; This represents dual-speed protection constraints, including requirements for emergency braking safety distance and loss-of-power coasting distance.

4. The simulation and optimization method for the operating speed curve of a maglev train according to claim 3, characterized in that, Step S3 includes: S31 via mapping function expression Calculate the next speed of the maglev train in traction mode. And the speed at which the maglev train reaches the next speed-limited zone in coasting mode. ; S32 If Then the maglev train is controlled to be in traction mode. ;like If so, the maglev train will be in cruise mode; if Then the maglev train is controlled to be in coasting mode. ;like Then the maglev train is controlled to be in braking mode. ; S33 Based on the maglev train operation mode judgment result obtained in sub-step S32, the formula is used... Update the traction and braking coefficients of the maglev train; where: It is a velocity-dependent single-step change, determined by the maximum acceleration impact rate constraint; It is the dot product of the operating mode vector and the direction control vector; the direction control vector The sign of each component is determined based on the current traction coefficient value and operating mode status of the maglev train, specifically through a combination of the following four sub-functions: Of the four functions mentioned above: Defined as the control function for traction mode, when When this time, it indicates that traction needs to be increased, and the vehicle should return. If the absolute value of the current coefficient is less than 1, then return a positive value. Increase; if it has reached 1, return to zero and remain unchanged; when When this is the case, it indicates that the traction force needs to be reduced and the vehicle needs to return. ,in It is an indicator function, in When the value is 1, it is 0 when the value is 0, ensuring... Decrease toward zero; when When the time indicates a non-traction state, returning to zero makes It does not change with the traction mode; Defined as the control function for cruise mode, when When, return ,drive To threshold Approach; It is the balance coefficient required for cruising, ensuring that traction equals drag; through gradual adjustment to ; The control function defined as lazy mode, when When, return ,drive Decrease toward zero; Defined as the control function for braking mode, when When, return ,make Increasing towards -1 increases braking force; when When, return This reduces the braking force until it reaches zero. S34 Through-type The resultant force acting on the maglev train is calculated; where: The updated traction coefficient; The maximum traction force is dependent on position and speed.

5. The simulation and optimization method for the operating speed curve of a maglev train according to claim 4, characterized in that, Step S4 includes: S41 Through Type Calculate the slope of the initial position state at a given time step. ; Through Calculate the slope of the velocity state at this initial point. In the formula: It is the current traction or braking force. and These are the basic resistance and the line resistance, respectively. It's about train quality; Through Calculate the slope of the energy consumption state at this initial point. ; Through Calculate the slope of the q-axis current state at this initial point. ; S42 Slope based on the initial point's position state The slope of the velocity state Slope of energy consumption state and the slope of the q-axis current state The slopes of the remaining position states are calculated using the RK4 method. The slope of the velocity state Slope of energy consumption state and the slope of the current state ; S43 Slope based on all position states The slope of the velocity state Slope of energy consumption state and the slope of the current state , through The operating status of the maglev train is updated by weighting and combining the four slopes. S44 uses a verification feedback mechanism. Determine whether the change in the operating state of the maglev train obtained in sub-execution step S43 is within the preset acceptable range. If so, repeat sub-steps S41 to S44 to calculate the operating state of the maglev train for the next time step. Otherwise, determine that the maglev train is in a high-speed operating state and execute sub-step S45. S45 Through-type The high-speed operating status of the maglev train is updated, and the spatial resolution is improved; where the slope of the position state is... The slope of the velocity state Slope of energy consumption state The slope of the current state The slope of the velocity state and the slope of time state Obtained by the RK4 method.

6. The simulation and optimization method for the operating speed curve of a maglev train according to claim 5, characterized in that, In step S3, the following constraints are added during each transition of the maglev train's operating state: Electrical parameter constraints, the conditional expression is: Passenger comfort constraints, including the following conditions: Formula for calculating acceleration impact rate Conditional expression for the change of single-step traction coefficient in time-domain discretization Conditional expression for the change of single-step traction coefficient in spatial discretization Dual-velocity protection constraints, the conditional expressions include: Inverse dynamic equations of the braking process Dynamic equations of unpowered gliding Glide distance constraints Speed ​​limit inflection point constraint, the condition is as follows: 。 7. The simulation and optimization method for the operating speed curve of a maglev train according to claim 5, characterized in that, In step S4, the process of adjusting the speed of the maglev train through the virtual speed limit generation mechanism includes: The maglev line is divided into R virtual speed-limited zones, each with a length of... Number of partitions Based on the total length of the line and partition length Decision, satisfaction In the formula, Indicates rounding up; Through Calculate and obtain virtual speed limit vectors for various operating conditions. ; The various operating conditions mentioned include: The maximum speed limit of the current partition is higher than that of the next partition. And it's not the first partition. ; The current partition has the same maximum speed limit as the previous partition. And it is in the intra-block cruise segment ; The current partition has the same maximum speed limit as the previous partition. And it is in the decreasing segment within the block. ; The maximum speed limit of the current partition is lower than that of the next partition. This indicates that you have entered a region with an increased speed limit. Set candidate solutions The virtual rate limit generation mechanism is invoked to generate a complete virtual rate limit configuration. ; The virtual speed limit configuration and fixed line vehicle parameters are input into the maglev train operation simulation process for calculation, so that the maglev train operation simulation process can simulate the train's operation process from the starting point to the destination according to the virtual speed limit and line conditions, generate detailed speed curves, and record the position, speed, running time, and energy consumption information of each state point. Extract runtime from the information of each recorded state point. and energy consumption ;, through formula Construct an objective function, and obtain candidate solutions by solving the objective function; where: It is a predefined runtime requirement. It is a weighting factor for runtime deviation, used to reflect the importance of on-time performance. It is the weighting coefficient for energy consumption; Determine whether the candidate solutions obtained by solving the objective function are infeasible; if so, return a maximal value of the objective function. And obtain the value sequence of the objective function. ; Based on the value sequence of the objective function, the first... generation Sort the nth candidate solution in ascending order to obtain an ordered sequence of solutions. Let the sorted nth solution be denoted as . The solution is ,in It is a sorting and permutation function that satisfies ; Through Select the first sorted items Each solution is considered as the set of optimal solutions; where... It is the optimal solution retention ratio parameter; Extract candidate solutions from the optimal solution set. All A virtual speed limit block ; Through Perform a random reorganization decision on a given virtual speed limit block, generating a uniformly distributed random number. And compare it with the threshold of 0.5: If Then retain the virtual speed limit block at the current position. Unchanged; otherwise, through formula Replace the virtual speed limit block at the current position with the virtual speed limit block at the next position. Obtain the recombined virtual speed limit block sequence Through For a certain virtual speed limit block after reorganization Update; where: It is the number of partitions within a certain reorganized virtual rate-limiting block; These are global control parameters; Through Generate a new virtual speed limit sequence to replace the recombined virtual speed limit block. ,get A new candidate solution is found, and the new candidate solution set is used. Express; Through Merge the new set of candidate solutions; Based on the merged solution Repeat step S4 based on the maximum number of iterations G to obtain the merged solution after multiple rounds; Through After multiple rounds of merging, the solution with the smallest objective function value is selected as the optimal solution.

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